# std::acosh, std::acoshf, std::acoshl

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< cpp‎ | numeric‎ | math

Defined in header `<cmath>` |  |
| (1) |
float acosh ( float num ); double acosh ( double num ); long double acosh ( long double num ); |  | (until C++23)
/*floating-point-type*/ acosh ( /*floating-point-type*/ num ); |  | (since C++23) (constexpr since C++26)
float acoshf( float num ); | (2) | (since C++11) (constexpr since C++26)
long double acoshl( long double num ); | (3) | (since C++11) (constexpr since C++26)
SIMD overload (since C++26) |  |
Defined in header `<simd>` |  |
template< /*math-floating-point*/ V > constexpr /*deduced-simd-t*/<V> acosh ( const V& v_num ); | (S) | (since C++26)
Additional overloads (since C++11) |  |
Defined in header `<cmath>` |  |
template< class Integer > double acosh ( Integer num ); | (A) | (constexpr since C++26)

1-3) Computes the inverse hyperbolic cosine of num. The library provides overloads of `std::acosh` for all cv-unqualified floating-point types as the type of the parameter.(since C++23)

S) The SIMD overload performs an element-wise `std::acosh` on v_num. (See `math-floating-point` and `deduced-simd-t` for their definitions.) | (since C++26)

A) Additional overloads are provided for all integer types, which are treated as double. | (since C++11)

### Parameters

num | - | floating-point or integer value

### Return value

If no errors occur, the inverse hyperbolic cosine of num (cosh-1
(num), or arcosh(num)) on the interval [0, +∞], is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

### Error handling

Errors are reported as specified in math_errhandling.

If the argument is less than 1, a domain error occurs.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- if the argument is less than 1, FE_INVALID is raised an NaN is returned.
- if the argument is 1, +0 is returned.
- if the argument is +∞, +∞ is returned.
- if the argument is NaN, NaN is returned.

### Notes

Although the C standard (to which C++ refers for this function) names this function "arc hyperbolic cosine", the inverse functions of the hyperbolic functions are the area functions. Their argument is the area of a hyperbolic sector, not an arc. The correct name is "inverse hyperbolic cosine" (used by POSIX) or "area hyperbolic cosine".

The additional overloads are not required to be provided exactly as (A). They only need to be sufficient to ensure that for their argument num of integer type, std::acosh(num) has the same effect as std::acosh(static_cast<double>(num)).

### Examples

Run this code

    #include <cerrno>
    #include <cfenv>
    #include <cfloat>
    #include <cmath>
    #include <cstring>
    #include <iostream>

    // #pragma STDC FENV_ACCESS ON

    int main()
    {
        std::cout << "acosh(1) = " << std::acosh(1) << '\n'
                  << "acosh(10) = " << std::acosh(10) << '\n'
                  << "acosh(DBL_MAX) = " << std::acosh(DBL_MAX) << '\n'
                  << "acosh(Inf) = " << std::acosh(INFINITY) << '\n';

        // error handling
        errno = 0;
        std::feclearexcept(FE_ALL_EXCEPT);

        std::cout << "acosh(0.5) = " << std::acosh(0.5) << '\n';

        if (errno == EDOM)
            std::cout << "    errno == EDOM: " << std::strerror(errno) << '\n';
        if (std::fetestexcept(FE_INVALID))
            std::cout << "    FE_INVALID raised\n";
    }

Possible output:

    acosh(1) = 0
    acosh(10) = 2.99322
    acosh(DBL_MAX) = 710.476
    acosh(Inf) = inf
    acosh(0.5) = -nan
        errno == EDOM: Numerical argument out of domain
        FE_INVALID raised

### See also

asinhasinhfasinhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic sine (\({\small\operatorname{arsinh}{x}}\)arsinh(x)) (function)
atanhatanhfatanhl (C++11)(C++11)(C++11) | computes the inverse hyperbolic tangent (\({\small\operatorname{artanh}{x}}\)artanh(x)) (function)
coshcoshfcoshl (C++11)(C++11) | computes hyperbolic cosine (\({\small\cosh{x}}\)cosh(x)) (function)
acosh(std::complex) (C++11) | computes area hyperbolic cosine of a complex number (\({\small\operatorname{arcosh}{z}}\)arcosh(z)) (function template)
C documentation for acosh

### External links

Weisstein, Eric W. "Inverse Hyperbolic Cosine." From MathWorld — A Wolfram Web Resource.

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